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Reliable Electrical Switching of Tri-State Antiferromagnetic Néel Order in $α$-Fe$_2$O$_3$ Epitaxial FilmsJun 11 2019The ability to manipulate antiferromagnetic (AF) moments is a key requirement for the emerging field of antiferromagnetic spintronics. Electrical switching of bi-state AF moments has been demonstrated in metallic AFs, CuMnAs and Mn$_2$Au. Recently, current-induced ... More

Anisotropic Magnetoresistance and Nontrivial Spin Magnetoresistance in Pt/$α$-Fe$_2$O$_3$ Bilayers: Evidence for Antiferromagnetic Proximity EffectJun 11 2019To date, magnetic proximity effect (MPE) has only been conclusively observed in ferromagnet (FM) based systems. We report the observation of anomalous Hall effect and anisotropic magnetoresistance in angular dependent magnetoresistance (ADMR) measurements ... More

Optimal Denial-of-Service Attack Energy Management over an SINR-Based NetworkOct 05 2018We consider a scenario in which a DoS attacker with the limited power resource jams a wireless network through which the packet from a sensor is sent to a remote estimator to estimate the system state. To degrade the estimation quality with power constraint, ... More

The 2D Linearly Polarized Near-Field Focusing Based on Angularly Discretized Slot ArraysApr 29 2014A 2-D near-field focusing design is proposed based on the circular slot array waveguide structures, synthesized using the array-factor theory, and demonstrated by full-wave simulations. The principle of beam-focusing is extended to the 2-D angularly discretized ... More

Anisotropic Magnetoresistance and Nontrivial Spin Magnetoresistance in Pt/$α$-Fe$_2$O$_3$ Bilayers: Evidence for Antiferromagnetic Proximity EffectJun 11 2019Jul 19 2019To date, magnetic proximity effect (MPE) has only been conclusively observed in ferromagnet (FM) based systems. We report the observation of anomalous Hall effect and anisotropic magnetoresistance in angular dependent magnetoresistance (ADMR) measurements ... More

Person re-identification via efficient inference in fully connected CRFJun 23 2015In this paper, we address the problem of person re-identification problem, i.e., retrieving instances from gallery which are generated by the same person as the given probe image. This is very challenging because the person's appearance usually undergoes ... More

Orbital Angular Momentum Generation and Detection by Geometric-Phase Based MetasurfacesMar 09 2018We present a comprehensive review on the geometric-phase based metasurfaces for orbital angular momentum(OAM) generation and detection. These metasurfaces manipulate the electromagnetic (EM) wave by introducing abrupt phase change, which is strongly dependent ... More

Pseudospin-Polarized Topological Line Defects in Dielectric Photonic CrystalsJul 10 2019Electromagnetic topological insulators have been explored extensively due to the robust edge states they support. In this work, we propose a topological electromagnetic system based on a line defect in topologically nontrivial photonic crystals (PCs). ... More

Programmable Active Janus Droplets Driven by Water/Alcohol Phase SeparationDec 23 2016We report the existence of self-propelled Janus droplets driven by phase separation, which are able to deliver cargo in a programmable manner. The self-propelling droplets are initially formed by a water/ethanol mixture in a squalane/monoolein solution, ... More

Automatic learner summary assessment for reading comprehensionJun 18 2019Automating the assessment of learner summaries provides a useful tool for assessing learner reading comprehension. We present a summarization task for evaluating non-native reading comprehension and propose three novel approaches to automatically assess ... More

Text Readability Assessment for Second Language LearnersJun 18 2019This paper addresses the task of readability assessment for the texts aimed at second language (L2) learners. One of the major challenges in this task is the lack of significantly sized level-annotated data. For the present work, we collected a dataset ... More

OGNet: Salient Object Detection with Output-guided Attention ModuleJul 17 2019Attention mechanisms are widely used in salient object detection models based on deep learning, which can effectively promote the extraction and utilization of useful information by neural networks. However, most of the existing attention modules used ... More

Approximating three-dimensional Navier-Stokes equations driven by space-time white noiseSep 17 2014In this paper we study approximations to 3D Navier-Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in [GIP13]. A solution theory for this equation has been developed recently in [ZZ14] based on regularity ... More

Three-dimensional Navier-Stokes equations driven by space-time white noiseMay 31 2014Jan 04 2017In this paper we study 3D Navier-Stokes (NS) equation driven by space-time white noise by using regularity structure theory introduced in [Hai14] and paracontrolled distribution proposed in [GIP13]. We obtain local existence and uniqueness of solutions ... More

Strong-Feller property for Navier-Stokes equations driven by space-time white noiseSep 27 2017Sep 29 2017In this paper we prove strong Feller property for the Markov semigroups associated to the two or three dimensional Navier-Stokes (N-S) equations driven by space-time white noise using the theory of regularity structures introduced by Martin Hairer in ... More

Lattice approximation to the dynamical $Φ_3^4$ modelAug 23 2015We study the lattice approximations to the dynamical $\Phi^4_3$ model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical $\Phi_3^4$ model in probability, locally ... More

Meson-baryon Scattering in Extend-on-mass-shell scheme at $\mathcal{O}(p^3)$Feb 09 2019In this present work, we study the scattering of a pseudoscalar meson off one ground state octet baryon in covariant baryon chiral perturbation theory up to the next-to-next-to-leading order. We remove the power counting breaking terms with the extended-on-mass-shell ... More

Meson-baryon Scattering in Extend-on-mass-shell scheme at $\mathcal{O}(p^3)$Feb 09 2019Feb 12 2019In this present work, we study the scattering of a pseudoscalar meson off one ground state octet baryon in covariant baryon chiral perturbation theory up to the next-to-next-to-leading order. We remove the power counting breaking terms with the extended-on-mass-shell ... More

A Wong-Zakai theorem for $Φ^4_3$ modelApr 16 2015We prove a version of the Wong-Zakai theorem for the dynamical $\Phi_3^4$ model driven by space-time white noise on $\mathbb{T}^3$. For the $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed in order to define the nonlinear ... More

Dimension reduction-based significance testing in nonparametric regressionOct 13 2015A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a local smoothing ... More

Piecewise linear approximation for the dynamical $Φ^4_3$ modelApr 16 2015Oct 22 2017We construct a piecewise linear approximation for the dynamical $\Phi_3^4$ model on $\mathbb{T}^3$ by the theory of regularity structures in [Hai14]. For the dynamical $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed ... More

Weak universality of the dynamical $Φ_3^4$ model on the whole spaceNov 04 2018Nov 06 2018We prove the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on $\mathbb{R}^3$ to the dynamical $\Phi^4_3$ model by paracontrolled distributions on weighted Besov space. Our approach depends on the delicate ... More

Dirichlet form associated with the $Φ_3^4$ modelMar 29 2017Jun 25 2017We construct the Dirichlet form associated with the dynamical $\Phi^4_3$ model obtained in [Hai14, CC13] and [MW16]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear form. As a consequence, this classical gradient ... More

Random attractor associated with the quasi-geostrophic equationMar 24 2013We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. $\alpha>1/2$) by proving the existence of a ... More

Three-dimensional Navier-Stokes equations driven by space-time white noiseMay 31 2014Jun 10 2015In this paper we study 3D Navier-Stokes (NS) equation driven by space-time white noise by using regularity structure theory introduced in [Hai14] and paracontrolled distribution proposed in [GIP13]. We obtain local existence and uniqueness of solutions ... More

A Deep-Learning-Based Fashion Attributes Detection ModelOct 24 2018Analyzing fashion attributes is essential in the fashion design process. Current fashion forecasting firms, such as WGSN utilizes information from all around the world (from fashion shows, visual merchandising, blogs, etc). They gather information by ... More

The higher sharpApr 02 2016Aug 02 2016We establish the descriptive set theoretic representation of the mouse $M_n^{#}$, which is called $0^{(n+1)#}$.

On Layered Erasure Interference Channels without CSI at TransmittersJan 24 2016This paper studies a layered erasure model for two-user interference channels, which can be viewed as a simplified version of Gaussian fading interference channel. It is assumed that channel state information~(CSI) is only available at receivers but not ... More

On the critical branching random walk II: Branching capacity and branching recurrenceDec 01 2016We continue our study of critical branching random walk and branching capacity. In this paper we introduce branching recurrence and branching transience and prove an analogous version of Wiener's Test.

Geometry and interior nodal sets of Steklov eigenfunctionsOct 25 2015We investigate the geometric properties of Steklov eigenfunctions in smooth manifolds. We derive the refined doubling estimates and Bernstein's inequalities. For the real analytic manifolds, we are able to obtain the sharp upper bound for the measure ... More

Dirichlet Problem of Quaternionic Monge-Ampère EquationsMar 13 2014Feb 11 2015In this paper, the author studies quaternionic Monge-Amp\`ere equations and obtains the existence and uniqueness of the solutions to the Dirichlet problem for such equations without any restriction on domains. Our paper not only answers to the open problem ... More

Colored HOMFLY polynomial via skein theoryJun 26 2012In this paper, we study the properties of the colored HOMFLY polynomials via HOMFLY skein theory. We prove some limit behaviors and symmetries of the colored HOMFLY polynomial predicted in some physicists' recent works.

Circular flow number of highly edge connected signed graphsNov 14 2012This paper proves that for any positive integer $k$, every essentially $(2k+1)$-unbalanced $(12k-1)$-edge connected signed graph has circular flow number at most $2+\frac 1k$.

A Sharp Height Estimate for the Spacelike Constant Mean Curvature Graph in the Lorentz-Minkowski SpaceAug 11 2015May 30 2016In this paper, based on the local comparison principle in [12], we study the local behavior of the difference of two spacelike graphs in a neighborhood of a second contact point. Then we apply it to the constant mean curvature equation in 3-dimensional ... More

Geometry and interior nodal sets of Steklov eigenfunctionsOct 25 2015Oct 03 2017We investigate the geometric properties of Steklov eigenfunctions in smooth manifolds. We derive the refined doubling estimates and Bernstein's inequalities. For the real analytic manifolds, we are able to obtain the sharp upper bound for the measure ... More

Electroweak results from the ATLAS and CMS experimentsSep 28 2015I summarize an extensive ATLAS and CMS electroweak physics program that involves a variety of single boson, diboson, triboson, and vector boson scattering measurements. The relevance of these studies to our understanding of the electroweak sector and ... More

Exploring Temporal Information for Improved Video UnderstandingMay 25 2019In this dissertation, I present my work towards exploring temporal information for better video understanding. Specifically, I have worked on two problems: action recognition and semantic segmentation. For action recognition, I have proposed a framework, ... More

A general detector testing system using cosmic raysAug 27 2013A cosmic ray hodoscope with two-dimensional spacial sensitivity and good time resolution has been developed. The system is designed to use the cosmic muons as probes to test the performances of charged particle sensitive detectors. This paper will present ... More

Optimal control of risk process in a regime-switching environmentSep 16 2010Dec 10 2010This paper is concerned with cost optimization of an insurance company. The surplus of the insurance company is modeled by a controlled regime switching diffusion, where the regime switching mechanism provides the fluctuations of the random environment. ... More

A New Framework for Ranking Vulnerabilities in the CloudsNov 23 2016Dec 06 2016Qualifying and ranking threat degrees of vulnerabilities in cloud service are known to be full of challenges. Although there have been several efforts aiming to address this problem, most of them are too simple or cannot be applied into cloud infrastructure. ... More

Super-symmetric informationally complete measurementsDec 02 2014Aug 23 2015Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately ... More

Quantum state estimation with informationally overcomplete measurementsApr 14 2014Aug 05 2014We study informationally overcomplete measurements for quantum state estimation so as to clarify their tomographic significance as compared with minimal informationally complete measurements. We show that informationally overcomplete measurements can ... More

Group structures of elementary supersingular abelian varieties over finite fieldsAug 31 1998Let A be a supersingular abelian variety over a finite field k. We give an approximate description of the structure of the group A(k) of rational points of A over k in terms of the characteristic polynomial f of the Frobenius endomorphism of A relative ... More

Affine Demazure modules and $T$-fixed point subschemes in the affine GrassmannianOct 27 2007Nov 20 2008Let $G$ be a simple algebraic group of type $A$ or $D$ defined over $\C$ and $T$ be a maximal torus of $G$. For a dominant coweight $\lambda$ of $G$, the $T$-fixed point subscheme $(\bar{Gr}_G^\lambda)^T$ of the Schubert variety $\bar{Gr}_G^\lambda$ in ... More

A Note on Equivariant K-stabilityJul 17 2019We define G-pseudovaluations on a variety with a group action G. By introducing G-pseudovaluations, we are able to give some criteria for G-equivariant K-stability of Fano varieties which are parallel to existing results for usual K-stability.

A Probability Method to Prove Combinatorial IdentitiesOct 30 2009A probability method is provided to prove three classes of combinatorial identities. The method is extremely simple, only one step after the proper probability setup.

The probability of Riemann's hypothesis being true is equal to 1Sep 24 2016Apr 26 2018Let $P$ be the set of all prime numbers, ${q_1},{q_2}, \cdots ,{q_m} \in P$, $P_k$ be the k-th $(k = 1,2, \cdots m)$ element of $P$ in ascending order of size, ${\alpha _1},{\alpha _2}, \cdots ,{\alpha _m}$ be positive integers, and ${\beta _1},{\beta ... More

On Dziobek Special Central ConfigurationsMay 11 2017Jun 02 2017We study the special central configurations of the curved N-body problem in S^3. We show that there are special central configurations formed by N masses for any N >2. We then extend the concept of special central configurations to S^n, n>0, and study ... More

Stable Cluster Core Detection in Correlated Hashtag GraphMar 02 2015Hashtags in twitter are used to track events, topics and activities. Correlated hashtag graph represents contextual relationships among these hashtags. Maximum clusters in the correlated hashtag graph can be contextually meaningful hashtag groups. In ... More

An upper bound for the probability of visiting a distant point by critical branching random walk in $\mathbb{Z}^4$Mar 01 2015Nov 27 2016In this paper, we study the probability of visiting a distant point $a\in \mathbb{Z}^4$ by critical branching random walk starting from the origin. We prove that this probability is bounded by $1/(|a|^2\log |a|)$ up to a constant.

Multi-Layer Cyber-Physical Security and Resilience for Smart GridSep 30 2018The smart grid is a large-scale complex system that integrates communication technologies with the physical layer operation of the energy systems. Security and resilience mechanisms by design are important to provide guarantee operations for the system. ... More

Kan replacement of simplicial manifoldsDec 22 2008Sep 03 2009We establish a functor $Kan$ from local Kan simplicial manifolds to weak Kan simplicial manifolds. It gives a solution to the problem of extending local Lie groupoids to Lie 2-groupoids.

Moduli Spaces of $J$-holomorphic Curves with General Jet ConstraintsNov 09 2009In this paper, we prove that the tagent map of the holomorphic $k$- jet evaluation $j^k_{hol}$ from the mapping space to holomorphic $k$-jet bundle, when restricted on the universal moduli space of simple J-holomorphic curves with one marked point, is ... More

The higher sharp III: An EM blueprint of $0^{3\#}$ and the level-4 Kechris-MartinMay 30 2017We establish the descriptive set theoretic representation of the mouse $M_n^{\#}$, which is called $0^{(n+1)\#}$. This part partially finishes the case $n=2$ by establishing the higher level analog of the EM blueprint definition of $0^{\#}$. From this, ... More

The higher sharp II: on $M_2^\#$Apr 19 2016Jun 06 2017We establish the descriptive set theoretic representation of the mouse $M_n^{\#}$, which is called $0^{(n+1)\#}$. This part partially deals with the case $n=2$ by proving the many-one equivalence of $M_2^{\#}$ and the theory of $L_{\boldsymbol{\delta}^1_3}[T_3]$ ... More

The higher sharp I: on $M_1^\#$Apr 02 2016May 30 2017We establish the descriptive set theoretic representation of the mouse $M_n^{\#}$, which is called $0^{(n+1)\#}$. This part deals with the case $n=1$.

Lightface mice with finitely many Woodin cardinals from optimal determinacy hypothesesOct 07 2016The determinacy of lightface $\Delta^1_{2n+2}$ and boldface $\boldsymbol{\Pi}^1_{2n+1}$ sets implies the existence of an $(\omega, \omega_1)$-iterable $M_{2n+1}^{\#}$.

The viability property of jump diffusion processes on Riemannian manifoldsMay 18 2010In this note, we consider the necessary and sufficient condition for viability property of diffusion processes with jumps on closed submanifolds of $R^{m}$ with some concrete examples.

Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes JumpsSep 22 2013Oct 14 2014In this paper, we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. ... More

Demystifying Core Ranking in Pinterest Image SearchMar 26 2018Pinterest Image Search Engine helps hundreds of millions of users discover interesting content everyday. This motivates us to improve the image search quality by evolving our ranking techniques. In this work, we share how we practically design and deploy ... More

Central Limit Theorem for Nonlinear Hawkes ProcessesApr 04 2012Oct 14 2014Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. In this paper, we obtain a functional central limit theorem ... More

High-jet relations of the heat kernel embedding map and applicationsAug 02 2013Aug 14 2013For any compact Riemannian manifold $(M,g)$ and its heat kernel embedding map $psi_t$ from M into $l^2$ constructed in [BBG], we study the higher derivatives of $psi_t$ with respect to an orthonormal basis at $x$ on $M$. As the heat flow time $t$ goes ... More

Entity-oriented spatial coding and discrete topological spatial relationsJan 15 2016Based on a newly proposed spatial data model - spatial chromatic model (SCM), we developed a spatial coding scheme, called full-coded ordinary arranged chromatic diagram (full-OACD). Full-OACD is a type of spatial tessellation, where space is partitioned ... More

Statistical Properties of Loss Rate Estimators in Tree TopologyAug 06 2015Mar 25 2016Three types of explicit estimators are proposed here to estimate the loss rates of the links in a network of the tree topology. All of them are derived by the maximum likelihood principle and proved to be either asymptotic unbiased or unbiased. In addition, ... More

Riemann Zeta Function Expressed as the Difference of Two Symmetrized Factorials Whose Zeros All Have Real Part of 1/2Aug 06 2012Aug 20 2012In this paper, some new results are reported for the study of Riemann zeta function $\zeta(s)$ in the critical strip $0<Re(s)<1$, such as $\zeta(s)$ expressed in a generalized Euler product only involving prime numbers. Particularly, some new absolutely ... More

Deep Learning for Automated Medical Image AnalysisMar 12 2019Medical imaging is an essential tool in many areas of medical applications, used for both diagnosis and treatment. However, reading medical images and making diagnosis or treatment recommendations require specially trained medical specialists. The current ... More

A Theorem on Frequency Function for Multiple-Valued Dirichlet Minimizing FunctionsJul 23 2006Jul 26 2006This paper discusses the frequency function of multiple-valued Dirichlet minimizing functions in the special case when the domain and range are both two dimensional. It shows that the frequency function must be of value k/2 for some nonnegative integer ... More

BSDE and generalized Dirichlet forms: the finite dimensional caseJan 16 2012We consider the following quasi-linear parabolic system of backward partial differential equations: $(\partial_t+L)u+f(\cdot,\cdot,u, \nabla u\sigma)=0$ on $[0,T]\times \mathbb{R}^d\qquad u_T=\phi$, where $L$ is a possibly degenerate second order differential ... More

An integral representation for Besov and Lipschitz spacesJan 15 2011It is well known that functions in the analytic Besov space $B_1$ on the unit disk $\D$ admits an integral representation $$f(z)=\ind\frac{z-w}{1-z\bar w}\,d\mu(w),$$ where $\mu$ is a complex Borel measure with $|\mu|(\D)<\infty$. We generalize this result ... More

Optimal dividend control for a generalized risk model with investment incomes and debit interestFeb 21 2011Sep 18 2012This paper investigates dividend optimization of an insurance corporation under a more realistic model which takes into consideration refinancing or capital injections. The model follows the compound Poisson framework with credit interest for positive ... More

The Z-cubes: a hypercube variant with small diameterSep 23 2015This paper introduces a new variant of hypercubes, which we call Z-cubes. The n-dimensional Z-cube $H_n$ is obtained from two copies of the (n-1)-dimensional Z-cube $H_{n-1}$ by adding a special perfect matching between the vertices of these two copies ... More

The stabilization of the Frobenius--Hecke traces on the intersection cohomology of orthogonal Shimura varietiesJan 29 2018The orthogonal Shimura varieties are associated to special orthogonal groups over $\mathbb Q$ of signature $(n,2)$ at infinity. We consider the intersection cohomology of their Baily--Borel compactifications, and prove a version of Morel's formula for ... More

On the asymptotic quantization error for the doubling measures on Moran setsAug 01 2019We study the quantization errors for the doubling probability measures $\mu$ which are supported on a class of Moran sets $E\subset\mathbb{R}^q$. For each $n\geq 1$, let $\alpha_n$ be an arbitrary $n$-optimal set for $\mu$ of order $r$ and $\{P_a(\alpha_n)\}_{a\in\alpha_n}$ ... More

Kawasaki-type Dynamics: Diffusion in the kinetic Gaussian modelApr 06 2002May 22 2002In this article, we retain the basic idea and at the same time generalize Kawasaki's dynamics, spin-pair exchange mechanism, to spin-pair redistribution mechanism, and present a normalized redistribution probability. This serves to unite various order-parameter-conserved ... More

Accreting Circumplanetary Disks: Observational SignaturesAug 27 2014Oct 06 2014I calculate the spectral energy distributions (SEDs) of accreting circumplanetary disks using atmospheric radiative transfer models. Circumplanetary disks only accreting at $10^{-10} M_{\odot} yr^{-1}$ around a 1 M$_{J}$ planet can be brighter than the ... More

Translation invariance of Fock spacesJan 21 2011We show that there is only one Hilbert space of entire functions that is invariant under the action of naturally defined weighted translations.

Computing log-likelihood and its derivatives for restricted maximum likelihood methodsAug 25 2016Recent large scale genome wide association analysis involves large scale linear mixed models. Quantifying (co)-variance parameters in the mixed models with a restricted maximum likelihood method results in a score function which is the first derivative ... More

Eigenvalue resolution of self-adjoint matricesApr 28 2015Oct 10 2016Resolution of a compact group action in the sense described by Albin and Melrose is applied to the conjugation action by the unitary group on self-adjoint matrices. It is shown that the eigenvalues are smooth on the resolved space and that the trivial ... More

A simple proof of the strong integrality for full colored HOMFLYPT invariantsMar 13 2016By using the HOMFLY skein theory. We prove a strong integrality theorem for the reduced colored HOMFLYPT invariants defined by a basis in the full HOMFLY skein of the annulus.

Max-Margin Nonparametric Latent Feature Models for Link PredictionJun 18 2012We present a max-margin nonparametric latent feature model, which unites the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction and automatically infer the unknown latent social dimension. ... More

Doubling property and vanishing order of Steklov eigenfunctionsJul 06 2014The paper is concerned with the doubling estimates and vanishing order of the Steklov eigenfunction on the boundary of a smooth boundary domain $\mathbb R^n$. The eigenfunction is given by a Dirichlet-to-Neumann map. We improve the doubling property shown ... More

Interior nodal sets of Steklov eigenfunctions on surfacesJul 02 2015Oct 20 2015We investigate the interior nodal sets $\mathcal{N}_\lambda$ of Steklov eigenfunctions on connected and compact surfaces with boundary. The optimal vanishing order of Steklov eigenfunctions is shown be $C\lambda$. The singular sets $\mathcal{S}_\lambda$ ... More

Higher Codimensional Alpha Invariants and Characterization of Projective SpacesMay 18 2018We generalize the definition of alpha invariant to arbitrary codimension. We also give a lower bound of these alpha invariants for K-semistable Q-Fano varieties and show that we can characterize projective spaces among all K-semistable Fano manifolds ... More

Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar CurvatureMar 14 2019We prove that the least area of the non-contractible immersed spheres is no more than $4\pi$ in any oriented compact manifold with dimension $n+2\leq 7$ which satisfies $R\geq 2$ and admits a map to $\mathbf S^2\times T^n$ with nonzero degree. We also ... More

Statistical inference for autoregressive models under heteroscedasticity of unknown formApr 06 2018Aug 09 2018This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator ... More

Quantitative uniqueness of solutions to parabolic equationsAug 06 2017We investigate the quantitative uniqueness of solutions to parabolic equations with lower order terms on compact smooth manifolds. Quantitative uniqueness is a quantitative form of strong unique continuation property. We characterize quantitative uniqueness ... More

Nodal sets of Robin and Neumann eigenfunctionsOct 30 2018We investigate the measure of nodal sets for Robin and Neumann eigenfunctions in the domain and on the boundary of the domain. A polynomial upper bound for the interior nodal sets is obtained for the Robin eigenfunctions in the smooth domain. For the ... More

Doubling inequality and nodal sets for solutions of bi-Laplace equationsFeb 16 2018Dec 19 2018We investigate the doubling inequality and nodal sets for the solutions of bi-Laplace equations. A polynomial upper bound for the nodal sets of solutions and their gradient is obtained based on the recent development of nodal sets for Laplace eigenfunctions ... More

The power operation structure on Morava E-theory of height 2 at the prime 3Oct 13 2012We give explicit calculations of the algebraic theory of power operations for a specific Morava E-theory spectrum and its K(1)-localization. These power operations arise from the universal degree-3 isogeny of elliptic curves associated to the E-theory. ... More

Davies type estimate and the heat kernel bound under the Ricci flowNov 23 2013Feb 08 2014We prove a Davies type double integral estimate for the heat kernel $H(y,t;x,l)$ under the Ricci flow. As a result, we give an affirmative answer to a question proposed by Chow etc.. Moreover, we apply the Davies type estimate to provide a new proof of ... More

Determining All Maximum Uniquely Restricted Matching in Bipartite GraphsSep 28 2010The approach mapping from a matching of bipartite graphs to digraphs has been successfully used for forcing set problem, in this paper, it is extended to uniquely restricted matching problem. We show to determine a uniquely restricted matching in a bipartite ... More

Note on "Hydrodynamic Phase Locking of Swimming Microorganisms"Aug 29 2009We make remarks on Elfring and Lauga's [{\it Phys. Rev. Lett.} {\bf 103}, 088101 (2009)] paper. The energy dissipation or viscous dissipation plays an important role in the phase-locked state.

On Theorem 6 in "Relative Entropy and the Multivariable Multidimensional Moment Problem" [Mar 2006 1052-1066]May 30 2018Jun 06 2018Matrix-valued covariance extension and multivariate spectral estimation are formulated as generalized moment problems in the "THREE" approach and its extensions. Under this context, we discuss Theorem 6 in \cite{Georgiou-06} concerning the bijectivity ... More

Propagation of Singularities for Gravity-Capillary Water WavesOct 22 2018We generalize the wavefront set of H\"ormander and the homogeneous wavefront set of Nakamura to the quasi-homogeneous wavefront set, which enables us to obtain the propagation of singularities for gravity-capillary water waves of finite depth. Consequences ... More

An improved axiomatic definition of information granulationAug 27 2009To capture the uncertainty of information or knowledge in information systems, various information granulations, also known as knowledge granulations, have been proposed. Recently, several axiomatic definitions of information granulation have been introduced. ... More

A quantitative approach to choose among multiple mutually exclusive decisions: comparative expected utility theoryJan 08 2018Mutually exclusive decisions have been studied for decades. Many well-known decision theories have been defined to help people either to make rational decisions or to interpret people's behaviors, such as expected utility theory, regret theory, prospect ... More

Beam Charge Measurement for the g2p/GEp experimentsJun 08 2016Jun 26 2016The g2p/GEp experiments used a solid NH3 polarized target, where the polarization of the target is sensitive to temperature and radiation. The beam current was limited to 5-100 nA during the experiment to avoid too much depolarization of target (The typical ... More

Solvability via viscosity solutions for a model of phase transitions driven by configurational forcesDec 29 2009Feb 04 2011In the present article, we are interested in an initial boundary value problem for a coupled system of partial differential equations arising in martensitic phase transition theory of elastically deformable solid materials, e.g., steel. This model was ... More

SIC~POVMs and Clifford groups in prime dimensionsMar 18 2010Jun 30 2010We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of ... More

Control of Three Dimensional Water WavesDec 17 2017We study the exact controllability for spatially periodic water waves with surface tension, by localized exterior pressures applied to free surfaces. We prove that in any dimension, the exact controllability holds within arbitrarily short time, for sufficiently ... More